Question 1

Find the indefinite integral. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

Use left endpoints and 8 rectangles to find the approximation of the area of the region between the graph of the function   and the x-axis over the interval   .Round your answer to the nearest integer. ​

Accepted Answer

A) 1,207 
B) 1,607 
C) 1,282 
D) 1,582 
E) 1,407 
A) 1,207 
B) 1,607 
C) 1,282 
D) 1,582 
E) 1,407

Question 3

Find the indefinite integral and check the result by differentiation. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 4

Find the area of the shaded region for the function   . ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

Find the area of the shaded region for the function   . ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

Find the indefinite integral. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

​Evaluate:   . ​

Accepted Answer

A) ​   
B) ​   
C) ​0 
D) ​The function is not integrable on the interval   . 
A) ​   
B) ​   
C) ​0 
D) ​The function is not integrable on the interval   .

Question 8

Find   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

​The graph of   consists of line segments and quarter circles as shown in the graph to the right.What is the value of   ?

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
A) ​   
B) ​   
C) ​   
D) ​

Question 10

The volume V in liters of air in the lungs during a five-second respiratory cycle is approximated by the model   ,where t is the time in seconds.Approximate the average volume of air in the lungs during one cycle.Round your answer to four decimal places. ​

Accepted Answer

A) 1.8651 liter 
B) 1.9967 liter 
C) 0.4133 liter 
D) 0.8270 liter 
E) 0.5346 liter 
A) 1.8651 liter 
B) 1.9967 liter 
C) 0.4133 liter 
D) 0.8270 liter 
E) 0.5346 liter

Question 11

Find the general solution of the differential equation below and check the result by differentiation. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

Write the following limit as a definite integral on the interval   ,where   is any point in the ith subinterval. ​   ​

Accepted Answer

A)    
B) ​
 
​ 
C)    
D)    
E)    
A)    
B) ​
 
​ 
C)    
D)    
E)

Question 13

The maker of an automobile advertises that it takes 7 seconds to accelerate from 30 kilometers per hour to 70 kilometers per hour.Assuming constant acceleration,compute the distance,in meters,the car travels during the 7 seconds.Round your answer to two decimal places. ​

Accepted Answer

A) 41.14 m 
B) 194.44 m 
C) 97.22 m 
D) 54.44 m 
E) 38.89 m 
A) 41.14 m 
B) 194.44 m 
C) 97.22 m 
D) 54.44 m 
E) 38.89 m

Question 14

Use the properties of summation and Theorem 5.2 to evaluate the sum. ​   ​

Accepted Answer

A) 729 
B) 756 
C) 1,296 
D) 1,404 
E) 162 
A) 729 
B) 756 
C) 1,296 
D) 1,404 
E) 162

Question 15

Solve the differential equation. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral. ​   ​

Accepted Answer

A) 81 
B) 40.5 
C) 6 
D) 135 
E) -67.5 
A) 81 
B) 40.5 
C) 6 
D) 135 
E) -67.5

Question 17

Evaluate the integral.   given,   ,   ,     .

Accepted Answer

A) 54 
B) 1,119 
C) 10 
D) 1,351 
E) 241 
A) 54 
B) 1,119 
C) 10 
D) 1,351 
E) 241

Question 18

Evaluate the definite integral   .Use a graphing utility to verify your results. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

​What is the average value of   on the closed interval   ? ​

Accepted Answer

A) ​6.181 
B) ​2.000 
C) ​1.819 
D) ​7.364 
A) ​6.181 
B) ​2.000 
C) ​1.819 
D) ​7.364

Question 20

Find the indefinite integral   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Find the indefinite integral.

Use left endpoints and 8 rectangles to find the approximation of the area of the region between the graph of the function and the x-axis over the interval .Round your answer to the nearest integer.

Find the indefinite integral and check the result by differentiation.

Find the area of the shaded region for the function .

Find the area of the shaded region for the function .

Find the indefinite integral.

Evaluate: .

Find .

The graph of consists of line segments and quarter circles as shown in the graph to the right.What is the value of ?

The volume V in liters of air in the lungs during a five-second respiratory cycle is approximated by the model ,where t is the time in seconds.Approximate the average volume of air in the lungs during one cycle.Round your answer to four decimal places.

Find the general solution of the differential equation below and check the result by differentiation.

Write the following limit as a definite integral on the interval ,where is any point in the i^th subinterval.

The maker of an automobile advertises that it takes 7 seconds to accelerate from 30 kilometers per hour to 70 kilometers per hour.Assuming constant acceleration,compute the distance,in meters,the car travels during the 7 seconds.Round your answer to two decimal places.

Use the properties of summation and Theorem 5.2 to evaluate the sum.

Solve the differential equation.

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.

Evaluate the integral. given, , , .

Evaluate the definite integral .Use a graphing utility to verify your results.

What is the average value of on the closed interval ?

Find the indefinite integral .

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Exam 5: Integration

Find the indefinite integral. ​ ​

Use left endpoints and 8 rectangles to find the approximation of the area of the region between the graph of the function and the x-axis over the interval .Round your answer to the nearest integer. ​

Find the indefinite integral and check the result by differentiation. ​ ​

Find the area of the shaded region for the function . ​ ​

Find the area of the shaded region for the function . ​ ​

Find the indefinite integral. ​ ​

​Evaluate: . ​

Find . ​

​The graph of consists of line segments and quarter circles as shown in the graph to the right.What is the value of ?

The volume V in liters of air in the lungs during a five-second respiratory cycle is approximated by the model ,where t is the time in seconds.Approximate the average volume of air in the lungs during one cycle.Round your answer to four decimal places. ​

Find the general solution of the differential equation below and check the result by differentiation. ​ ​

Write the following limit as a definite integral on the interval ,where is any point in the ith subinterval. ​ ​

The maker of an automobile advertises that it takes 7 seconds to accelerate from 30 kilometers per hour to 70 kilometers per hour.Assuming constant acceleration,compute the distance,in meters,the car travels during the 7 seconds.Round your answer to two decimal places. ​

Use the properties of summation and Theorem 5.2 to evaluate the sum. ​ ​

Solve the differential equation. ​ ​

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral. ​ ​

Evaluate the integral. given, , , .

Evaluate the definite integral .Use a graphing utility to verify your results. ​

​What is the average value of on the closed interval ? ​

Find the indefinite integral . ​

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Find the indefinite integral.

Use left endpoints and 8 rectangles to find the approximation of the area of the region between the graph of the function and the x-axis over the interval .Round your answer to the nearest integer.

Find the indefinite integral and check the result by differentiation.

Find the area of the shaded region for the function .

Find the area of the shaded region for the function .

Find the indefinite integral.

Evaluate: .

Find .

The graph of consists of line segments and quarter circles as shown in the graph to the right.What is the value of ?

The volume V in liters of air in the lungs during a five-second respiratory cycle is approximated by the model ,where t is the time in seconds.Approximate the average volume of air in the lungs during one cycle.Round your answer to four decimal places.

Find the general solution of the differential equation below and check the result by differentiation.

Write the following limit as a definite integral on the interval ,where is any point in the i^th subinterval.

The maker of an automobile advertises that it takes 7 seconds to accelerate from 30 kilometers per hour to 70 kilometers per hour.Assuming constant acceleration,compute the distance,in meters,the car travels during the 7 seconds.Round your answer to two decimal places.

Use the properties of summation and Theorem 5.2 to evaluate the sum.

Solve the differential equation.

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.

Evaluate the definite integral .Use a graphing utility to verify your results.

What is the average value of on the closed interval ?

Find the indefinite integral .